Question

Take two multiples of any number. Find their lcm
What is your observation?​

Answer 1

What is your observation? Take two multiples of any number. What is their LCM?

Let the number be x and let the two multiples of x be ax and bx.

So, we come down to finding the LCM of ax and bx.

Since x is common to both, we need to consider it just once and that leaves a and b. At this point, there are 2 possibilities:

a and b are relatively prime i. e. GCD(a, b) = 1. In this case, the LCM of ax and bx is simply x*a*b.

a and b are not relatively prime i. e. they share a common multiple, say k, which in other words is GCD(a, b) = k. In this case, the LCM of ax and bx is x*a*b / k.

Very generically, the answer for LCM of ax and bx could be given as:

(x*a*b) / GCD(a,b). If GCD is 1 then it’s case 1 else it’s case 2.